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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    Coefficient of\[x\]in \[f(x)=\left| \begin{matrix}    x & {{(1+\sin x)}^{3}} & \cos x  \\    1 & \log (1+x) & 2  \\    {{x}^{2}} & {{(1+x)}^{2}} & 0  \\ \end{matrix} \right|\] is

    A)  0

    B)  1

    C)  - 2

    D)  Cannot be determined

    Correct Answer: C

    Solution :

    Coefficient\[x\]in\[f(x)\]is equal to coefficient of\[x\]in \[\left| \begin{matrix}    x & {{(1+x-\frac{{{x}^{3}}}{3!}...)}^{3}} & 1-\frac{{{x}^{2}}}{2!}  \\    1 & x-\frac{{{x}^{2}}}{2} & 2  \\    {{x}^{2}} & 1+{{x}^{2}} & 0  \\ \end{matrix} \right|\] coefficient of\[x\]in\[\left| \begin{matrix}    x & 1 & 1  \\    1 & x & 2  \\    {{x}^{2}} & 1 & 0  \\ \end{matrix} \right|\] = Coefficient of\[x\]in\[[x(0-2)-1(0-2{{x}^{2}})\]                                                                               \[+1(1-{{x}^{3}})]\]                 = - 2


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